High‐throughput FPGA implementation for quadratic unconstrained binary optimization

Abstract

AbstractQuadratic unconstrained binary optimization (QUBO) is a combinatorial optimization problem. Since various NP‐hard problems such as the traveling salesman problem can be formulated as a QUBO instance, QUBO is used with a wide range of applications. The main contribution of this article is to propose high‐throughput FPGA implementations for the QUBO solver. We perform the local search using different bit‐selection strategies based on the simulated annealing in the proposed implementation. The hardware is a pipeline structure with no pipeline hazards using multiple instances, where the bit‐flip operation is always performed every clock cycle. We implemented the proposed circuit on Xilinx UltraScale+ FPGA VU9P. The implementation result shows that the circuit can search solutions per second. Besides, by sharing the block RAM that stores a weight matrix, we implemented a dual annealer architecture that has two QUBO solvers into the FPGA. As a result, the dual annealer architecture can search solutions per second.